1205743997856÷666+143-987×987
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Introduction to the Problem
In this article, we will delve into the world of mathematics and explore a complex expression: 1205743997856÷666+143-987×987. This expression involves various mathematical operations, including division, addition, subtraction, and multiplication. Our goal is to simplify this expression and arrive at a final answer.
Understanding the Order of Operations
Before we begin simplifying the expression, it's essential to understand the order of operations. The order of operations is a set of rules that dictate the order in which mathematical operations should be performed. The acronym PEMDAS is commonly used to remember the order of operations:
- Parentheses: Evaluate expressions inside parentheses first.
- Exponents: Evaluate any exponential expressions next.
- Multiplication and Division: Evaluate any multiplication and division operations from left to right.
- Addition and Subtraction: Finally, evaluate any addition and subtraction operations from left to right.
Breaking Down the Expression
Let's break down the given expression into smaller parts and simplify each part step by step.
Part 1: 1205743997856÷666
To simplify this part, we need to perform the division operation.
result = 1205743997856 / 666
Using a calculator or performing the division manually, we get:
result = 1809999999.999999
Part 2: 143
This part is already simplified, so we can move on to the next part.
Part 3: -987×987
To simplify this part, we need to perform the multiplication operation.
result = -987 * 987
Using a calculator or performing the multiplication manually, we get:
result = -971,569
Combining the Parts
Now that we have simplified each part, we can combine them to get the final result.
final_result = 1809999999.999999 + 143 - 971,569
Final Calculation
Let's perform the final calculation:
final_result = 1809999999.999999 + 143 - 971,569
final_result = 1809999999.999999 + 143 - 971,569
final_result = 1809999999.999999 - 971,426
final_result = 1809999999.999999 - 971,426
final_result = 1809999990.573573
Conclusion
In this article, we simplified the complex expression 1205743997856÷666+143-987×987 by breaking it down into smaller parts and performing each operation step by step. We used the order of operations to guide us through the simplification process. The final result is 1809999990.573573.
Frequently Asked Questions
Q: What is the order of operations?
A: The order of operations is a set of rules that dictate the order in which mathematical operations should be performed. The acronym PEMDAS is commonly used to remember the order of operations.
Q: How do I simplify a complex expression?
A: To simplify a complex expression, break it down into smaller parts and perform each operation step by step, following the order of operations.
Q: What is the final result of the expression 1205743997856÷666+143-987×987?
A: The final result of the expression 1205743997856÷666+143-987×987 is 1809999990.573573.
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Introduction to the Problem
In this article, we will delve into the world of mathematics and explore a complex expression: 1205743997856÷666+143-987×987. This expression involves various mathematical operations, including division, addition, subtraction, and multiplication. Our goal is to simplify this expression and arrive at a final answer.
Understanding the Order of Operations
Before we begin simplifying the expression, it's essential to understand the order of operations. The order of operations is a set of rules that dictate the order in which mathematical operations should be performed. The acronym PEMDAS is commonly used to remember the order of operations:
- Parentheses: Evaluate expressions inside parentheses first.
- Exponents: Evaluate any exponential expressions next.
- Multiplication and Division: Evaluate any multiplication and division operations from left to right.
- Addition and Subtraction: Finally, evaluate any addition and subtraction operations from left to right.
Breaking Down the Expression
Let's break down the given expression into smaller parts and simplify each part step by step.
Part 1: 1205743997856÷666
To simplify this part, we need to perform the division operation.
result = 1205743997856 / 666
Using a calculator or performing the division manually, we get:
result = 1809999999.999999
Part 2: 143
This part is already simplified, so we can move on to the next part.
Part 3: -987×987
To simplify this part, we need to perform the multiplication operation.
result = -987 * 987
Using a calculator or performing the multiplication manually, we get:
result = -971,569
Combining the Parts
Now that we have simplified each part, we can combine them to get the final result.
final_result = 1809999999.999999 + 143 - 971,569
Final Calculation
Let's perform the final calculation:
final_result = 1809999999.999999 + 143 - 971,569
final_result = 1809999999.999999 + 143 - 971,569
final_result = 1809999999.999999 - 971,426
final_result = 1809999999.999999 - 971,426
final_result = 1809999990.573573
Conclusion
In this article, we simplified the complex expression 1205743997856÷666+143-987×987 by breaking it down into smaller parts and performing each operation step by step. We used the order of operations to guide us through the simplification process. The final result is 1809999990.573573.
Frequently Asked Questions
Q: What is the order of operations?
A: The order of operations is a set of rules that dictate the order in which mathematical operations should be performed. The acronym PEMDAS is commonly used to remember the order of operations.
Q: How do I simplify a complex expression?
A: To simplify a complex expression, break it down into smaller parts and perform each operation step by step, following the order of operations.
Q: What is the final result of the expression 1205743997856÷666+143-987×987?
A: The final result of the expression 1205743997856÷666+143-987×987 is 1809999990.573573.
Q: Can I use a calculator to simplify the expression?
A: Yes, you can use a calculator to simplify the expression. However, it's essential to understand the order of operations and perform each operation step by step to ensure accuracy.
Q: What if I make a mistake while simplifying the expression?
A: If you make a mistake while simplifying the expression, go back to the previous step and re-evaluate the operation. Make sure to follow the order of operations and perform each operation step by step.
Q: Can I use a computer program to simplify the expression?
A: Yes, you can use a computer program to simplify the expression. Many programming languages, such as Python and Java, have built-in functions for performing mathematical operations.
Q: How do I know if the expression is correct?
A: To verify the correctness of the expression, plug in the values and perform the operations manually. Compare the result with the final answer to ensure accuracy.
Q: Can I use this method to simplify other complex expressions?
A: Yes, you can use this method to simplify other complex expressions. The key is to break down the expression into smaller parts and perform each operation step by step, following the order of operations.
Q: What if the expression involves fractions or decimals?
A: If the expression involves fractions or decimals, perform the operations as usual, but make sure to follow the order of operations. You can also use a calculator or computer program to simplify the expression.
Q: Can I use this method to simplify expressions with exponents?
A: Yes, you can use this method to simplify expressions with exponents. The key is to evaluate the exponents first, then perform the remaining operations.
Q: What if the expression involves negative numbers?
A: If the expression involves negative numbers, perform the operations as usual, but make sure to follow the order of operations. You can also use a calculator or computer program to simplify the expression.
Q: Can I use this method to simplify expressions with variables?
A: Yes, you can use this method to simplify expressions with variables. The key is to substitute the values of the variables and perform the operations as usual.
Q: What if the expression involves multiple operations with the same precedence?
A: If the expression involves multiple operations with the same precedence, perform the operations from left to right.